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Exponential stability with respect to part of the variables for a class of nonlinear stochastic systems with Markovian switchings

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  • Socha, Leslaw
  • Zhu, Quanxin

Abstract

This paper deals with the exponential stability problem with respect to part of the variables of a class of nonlinear stochastic systems for three classes of Markovian switching processes. The methodologies of stability of stochastic hybrid systems and stability with respect to part of the variables based on Lyapunov methods are combined to find sufficient conditions of the exponential yp-stability for a class of nonlinear stochastic systems. Moreover, the detailed analysis and criteria of exponential mean square y-stability based on LMI methodology are also given for the case of linear systems.

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  • Socha, Leslaw & Zhu, Quanxin, 2019. "Exponential stability with respect to part of the variables for a class of nonlinear stochastic systems with Markovian switchings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 2-14.
    • Handle: RePEc:eee:matcom:v:155:y:2019:i:c:p:2-14
    DOI: 10.1016/j.matcom.2017.09.002
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    References listed on IDEAS

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    1. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
    2. Ignatyev, Oleksiy, 2009. "Partial asymptotic stability in probability of stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 597-601, March.
    3. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Li, Xiaodong & Li, Haitao & Li, Yalu & Yang, Xinrong, 2020. "Function perturbation impact on stability in distribution of probabilistic Boolean networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 1-12.
    2. Gaizhen Chang & Tingkun Sun & Zhiguo Yan & Min Zhang & Xiaomin Zhou, 2022. "Quantitative Mean Square Exponential Stability and Stabilization of Linear Itô Stochastic Markovian Jump Systems Driven by Both Brownian and Poisson Noises," Mathematics, MDPI, vol. 10(13), pages 1-16, July.

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